Fig. 1. Diagrammatic representation of the effective aerial and contact times, and vertical displacements. The vertical displacement of the centre of mass during the time of contact with the ground t_c (continuous line) and during the aerial phase t_a (broken line) is divided into a lower part S_ce (red) taking place when the vertical force is greater than body weight, and into an upper part S_ae (blue) taking place when the vertical force is less than body weight. Running speed increases from top to bottom. Note that in all cases S_ce (red) represents the amplitude of the oscillation of the spring–mass system from its equilibrium point and its duration t_ce represents a half period of the oscillation (neither the peak-to-peak vertical displacement nor the vertical displacement during contact represent the amplitude of the oscillation). S_ae (blue) represents the amplitude of the oscillation in the opposite direction, and its duration t_ae the half period of the oscillation, only at the lowest running speed (A) when the whole vertical displacement takes place during contact S_c. Only A, when no aerial phase takes place, is consistent with the spring–mass model. With increasing speed a progressively greater fraction of the vertical displacement takes place during the aerial phase S_a. The resonant frequency of the spring–mass system f_s=1/(2t_ce) equals the step frequency f only when t_ce=t_ae, i.e. when the rebound is symmetric (A,B). At high running speeds (C) the rebound is asymmetric (t_ce<t_ae) and the step frequency is lower than the resonant frequency of the system.